The parallelogram is considered the fundamental figure of Euclidean geometry. It is the simplest geometric figure of uniform generalization in any of the three spatial dimensions.
A parallelogram is a quadrilateral with two pairs of parallel sides. A parallelogram has both vertical and horizontal lines, and it’s always a square figure. The word “parallelogram” is derived from the Greek words “para” meaning “alongside” and “alograptos” meaning “writing tablet.” Because of its characteristics, the parallelogram is also known as an “oblong.”
In geometry, a parallelogram is a quadrilateral where both pairs of opposite sides are parallel and of equal length. It can also be classified as a quadrilateral with four angles and the opposite angles being congruent. The parallelograms are named for their parallel sides; they are also known as quadrilaterals, trapezia, or rhombi. A parallelogram has 4 vertices and 4 sides.
In its classic form, a parallelogram has two parallel sides which are equal in length to each other. It also has two opposite sides which are at right angles to the two parallel sides. The two sets of opposite sides are perpendicular to each other. Thus below are some of the properties of a parallelogram.
- Opposite sides are parallel- The opposite sides of a parallelogram are parallel to each other. Moreover, a parallelogram is symmetrical when one pair of opposite sides are of different lengths. Symmetry means that the same angle exists on both pairs of opposite sides, no angle exists on both pairs of the same sides. All 4 angles must be equal on both sides. An asymmetrical parallelogram is called a squished square or truncated square. Symmetrical parallelograms are squares or parallelograms which have the same sides and are congruent and have equal angles.
- Opposite angles are congruent- One unique property of a parallelogram is that if you divide one of its sides by the other side, they will be equal. The distance between the two sides is always a multiple of two (2,3,4, etc.). This is because of the perpendicular bisectors, or from each of the three sides (180°, 90°, and 60°). These perpendicular bisectors intersect at two points on the parallelogram. So, if one of the two sides of the parallelogram has the same length, they are equal. The other diagonal side is not equal to the other two sides.
- The two diagonals bisect each other- A parallelogram is a rectangle with two pairs of parallel sides. In addition, the two diagonals bisect each other and form four right angles. It is useful when we want to find the area or perimeter of a parallelogram.
Looking at the sides of a parallelogram, you can see that the perimeter is equal to 2 times the sum of the adjacent sides. It has a common angle with the north and south sides, and the opposite pair of sides. It has two opposite sides and a point opposite to the midpoint of each pair of opposite sides.
P = 2(a + b)
where, a = side and b= base
The area of parallelogram is equal to the product of the base and height of a parallelogram.
Because the two sides are congruent, you can just as well use the area of the shorter right and left sides. Thus, the area of a parallelogram is the base times the height. It can be used to express the area of other shapes in terms of linear measurements.
A = bh
where, b= base and h = height
A parallelogram is a quadrilateral whose opposite sides and adjacent sides form two pairs of parallel lines. To understand and learn more about parallelograms, visit Cuemath. They are one of the best online platforms for learning math and coding.